Let $f : [0, 2\pi] \rightarrow \mathbb{R}$ be given by $f(x) = \sum\limits_{n=1}^{\infty} \frac{\cos(nx)}{n^2}$. I already know that $f$ is differentiable on $(0, 2\pi)$ and that $f^{\prime}(x) = -\sum\limits_{n=1}^{\infty} \frac{\sin(nx)}{n}$ there.
What about $0$ and $2\pi$? Is it differentiable at those points?
